Some properties of $I_3$-λ-statistical cluster points




λ-statistical convergence, Ideal convergence, Triple sequence


In this note, we investigate some problems concerning the set of λ-statistical cluster points of triple sequences via ideals in finite dimensional spaces, and some of its properties in finite dimensional Banach spaces are proved.


Download data is not yet available.


F. Başar. (2012). Summability theory and its applications. Bentham Science Publishers, İstanbul.

Connor, J., Ganichev, M., Kadets, V. (2000). A Characterization of Banach Spaces with separable duals via weak statistical convergence. Journal of Mathematical Analysis and Applications, 244, 251-261.

Das, P., Dutta, S., Mohiuddine, S.A., Alotaibi, A. (2014). A-statistical cluster points in finite dimensional spaces and application to turnpike theorem. Abstract and Applied Analysis, Volume 2014, Article ID 354846, 7 pages.

Das, P., Savaş, E., Ghosal, S.K. (2011). On generalizations of certain summability methods using ideals. Applied Mathematics Letters, 24 (9), 1509-1514.

Demirci, I.A., Gürdal, M. (2022). On Lacunary Statistical ϕ ̃-convergence for Triple Sequences of Sets Via Ideals. Journal of Applied Mathematics and Informatics, 40 (3-4), 433-444.

Esi, A. (2013). λ_3-statistical convergence of triple sequences on probabilistic normed space. Global Journal of Mathematical Analysis, 1 (2), 29-36.

Esi, A., Savaş, E. (2015). On lacunary statistically convergent triple sequences in probabilistic normed space. Applied Mathematics & Information Sciences, 9 (5), 2529-2534.

Fast, H. (1951). Sur la convergence statistique. Colloquium Mathematicae, 2, 241-244.

Fridy, J.A. (1993). Statistical limit points. Proceedings of the American Mathematical Society, 4, 1187-1192.

Gürdal, M. (2004). Some type of convergence. Doctoral Dissertation, Sleyman Demirel University, Isparta.

Gürdal, M., Huban, M.B. (2014). On I-convergence of double sequences in the topology induced by random 2-norms. Matematicki Vesnik, 66 (1), 73-83.

Gürdal, M., Şahiner, A. (2008). Extremal I -limit points of double sequences. Applied Mathematics E-Notes, 8, 131-137.

Huban, M.B., Gürdal, M. (2021). Wijsman lacunary invariant statistical convergence for triple sequences via Orlicz function. Journal of Classical Analysis, 17 (2), 119-128.

Huban, M.B., Gürdal, M., Savaş, E. (2020). I-statistical limit superior and I -statistical limit inferior of triple sequences. 7th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM2020), Proceeding Book of ICRAPAM, 42-49.

Kostyrko, P., Macaj, M., Šalát, T. (2000). I -Convergence. Real Analysis Exchange, 26 (2), 669-686.

Mohiuddine, S.A., Hazarika, B., Alotaibi, A. (2017). On statistical convergence of double sequences of fuzzy valued functions. Journal of Intelligent & Fuzzy Systems, 32 (6), 4331-4342.

Mursaleen, M. (2000). λ-statistical convergence. Mathematica Slovaca, 50, 111-115.

Mursaleen, M., Edely, O.H.H. (2003). Statistical convergence of double sequences. Journal of Mathematical Analysis and Applications, 288, 223-231.

Nabiev, A., Pehlivan, S., Gürdal, M. (2007). On I-Cauchy sequences. Taiwanese Journal Mathematics, 11 (2), 569-576.

Pehlivan, S., Güncan, A., Mamedov, M.A. (2004). Statistical cluster points of sequences in finite dimensional spaces. Czechoslovak Mathematical Journal, 54 (1), 95-102.

Pehlivan, S., Gürdal, M., Fisher, B. (2006). Lacunary statistical cluster points of sequences. Math. Commun., 11, 39-46.

Şahiner, A., Gürdal, M., Düden, F.K. (2007). Triple sequences and their statistical convergence. Selçuk Journal of Applied Mathematics, 8 (2), 49-55.

Şahiner, A., Tripathy, B.C. (2008). Some I-related properties of triple sequences. Selçuk Journal of Applied Mathematics, 9 (2), 9-18.

Subramanian, N., Esi, A. (2018). Wijsman rough lacunary statistical convergence on I-Cesàro triple sequences. International Journal of Analysis and Applications, 16 (5), 643-653.

Yaying, T., Hazarika, B. (2020). Lacunary arithmetic statistical convergence. National Academy Science Letters, 43, 547-551.




How to Cite

Gürdal, V., & Kişi, Ömer. (2022). Some properties of $I_3$-λ-statistical cluster points. Dera Natung Government College Research Journal, 7(1), 10–19.